1. Field of the Invention
The present invention relates to a modelling method allowing more rapid obtaining of physical parameters of a geologic sample from experimental results obtained by subjecting the sample to centrifugation.
2. Description of the Prior Art
A well-known method for rapidly determining both the capillary pressure curves and the relative permeability curves of a porous rock sample initially saturated with a first fluid essentially consists in subjecting the sample to centrifugation in order to displace the fluid in place by means of another fluid.
Centrifugation devices such as those described in U.S. Pat. No. 5,463,894, French Patent 2,763,690, and U.S. Pat. No. 6,185,985 filed by the Assignee are for example used.
The sample initially saturated with a liquid A (brine for example) is placed in an elongate vessel or cup containing another fluid B of different density (oil for example). The vessel is fastened to the end of a rotating arm and a centrifugal force is applied thereto so as to study the displacements of the fluids in the sample during at least two distinct stages. During a first drainage stage, the assembly is subjected to a centrifugal force exerted along the length of the vessel so as to exert thereon an expulsion force which tends to cause part of first fluid A to flow out. Simultaneously, part of fluid A penetrates the sample. The two fluids move in the sample to a position of equilibrium where the force due to the capillary pressure in the pores makes up for the centrifugal force exerted. A measuring sonde is placed in the vessel, on the side of the sample. The sonde can be a capacitive type sonde for example, and it can comprise a metal rod insulated by means of a ceramic sheath. The capacitance between the rod and the conducting fluid (brine), which is proportional to the height immersed, is measured. With this system, the measuring accuracy is 1.5% of the pore volume. The sonde detects the position of the interface between the two liquids in the vessel and transmits the measurement signals to a signal acquisition and control device comprising hydraulic liquid circulation means and an acquisition device.
The various points of the capillary pressure curve (Pc) are obtained from measurement of the mean saturation of the sample at equilibrium for given rotating speeds. Determination of the relative permeability curves (Kr) is achieved by means of the saturation variation with time between two (transient) speed stages. None of these curves is obtained directly; the first one must be calculated and the second one requires a numerical flow simulator comprising (FIG. 11) a simulation module which reproduces the effects of the experiment by means of a numerical model, and an inversion module allowing to determine capillary pressure and relative permeability curves by iterative adjustment of an initial numerical model to the experimental results.
An example of a well-known flow simulator is the ACEX flow simulator based on Darcy""s generalized equations, which is described in:
Chardaire-Rivixc3xa8re, C.; 1992, Improving the Centrifuge Technique by Measuring Local Saturations; SPE 24882.
Although the centrifugation technique is widely used in the petroleum industry, because of its relative rapidity in relation to other existing methods, some implementation difficulties remain concerning determination of the capillary pressure curve as well as the relative permeability curves.
For a given speed stage, the transient state is difficult to determine since a very slow production stabilization is observed. Search for this equilibrium leads to long-lasting operations spread over several weeks, whose implementation presents practical difficulties, considering especially the often high rotating speed of the centrifuge. Furthermore, the time required therefore is even longer if one tries to increase the pore volume of the sample (by increasing the length thereof) in order to improve the saturation measuring accuracy.
Inversion, i.e. adjustment of a numerical model to experimental results, is difficult to achieve because the information relating to the relative permeabilities is concentrated on the transient part of the production curve, i.e. in a narrow range of experimental values. The acceleration applied to the centrifuge has a preponderant effect on the form of this transient part, notably its duration. Parallel determination of the capillary pressure curve leads to applying several constant speed stages rather than a long acceleration, which reduces the transient curves.
The modelling method according to the invention allows obtaining, with a considerable gain in time, the values of physical parameters of a geologic sample initially saturated with a first fluid placed in a vessel and subjected to centrifugation in the presence of a second fluid.
It comprises measuring the amount of fluids displaced by centrifugation and establishing saturation curves, at fixed time intervals, and comprises, for each rotating speed stage, modelling of a saturation curve best adjusting, at each time interval, to the curve portion already obtained and corresponding to the various previous measurements, the value of the saturation at equilibrium being deduced from characteristics of the modelled curve.
For each speed stage, an exponential type saturation curve is modelled by adjusting parameters, one of these parameters corresponding to the value of the saturation at equilibrium. The saturation curve is modelled for example by means of a sum of exponential functions depending on the adjustment parameters.
Centrifugation speeds allowing obtaining an even distribution of points on each saturation curve are preferably selected.
According to an embodiment, the method further comprises:
using a flow simulator for modelling a relation between the relative permeability values in relation to the two fluids for a sample of determined dimensions and permeability, and the saturation values in relation to these fluids according to various coefficients, and establishing a database connecting parameters intended for adjustment to the coefficients, for several saturation values in relation to at least one of the fluids, and
determining relative permeabilities of the sample subjected to centrifugation with reference to correspondence values extracted from the database.
The method has applications in the field of petrophysics where knowledge of parameters such as the capillary pressure, the relative permeability curves of porous rocks, allow reservoir engineers to characterize the flow conditions of hydrocarbons in a reservoir, to make production predictions and to elaborate development strategies.